Koopman-based Modeling for Rocket Landing Guidance Applications

In the last years, the need for an efficient way to solve precisely the rocket landing guidance problem has emerged as crucial for reusability purposes. In this context, Koopman Operator Theory is promising because of its ability to globally linearize dynamical systems by lifting the state into a subspace of observables. More recent studies show that it is beneficial, in terms of accuracy, to learn a dictionary of observables through neural network optimization. In this work, we address the atmospheric, fuel-optimal, rocket landing problem to assess if a Koopman model can be used to efficiently solve the corresponding Optimal Control Problem. The main contributions of this work are the extension of dictionary learning techniques to include control and the formulation of a new framework to estimate a bilinear control model, after obtaining the equivalent linear modeling of the free dynamics. We show that dictionary learning methods provide more accurate linear control models than state-of-the-art Koopman-related methods, such that they can be used to efficiently build and solve a representative Linear Programming Problem. We also show that the adoption of a bilinear control model is possible, but this approach leads to a significant decrease in the related computational efficiency.